I know way too much about hypermobility.
I was a talented dancer. I was made to give it up because 'your joints'.
I was good at gymnastics. I was made to give it up because 'your joints'.
I wasn't allowed to play football because 'your joints'.
I wasn't allowed to take the stabilisers off my bike because 'your joints'.
I wasn't allowed any weightbearing exercise because 'your joints'.
I wasn't allowed to go swimming because 'your joints'.
I wasn't allowed to run, jump, climb, play out with my friends because 'your joints'.
So I lost muscle tone. The loss of muscle tone made my joints more unstable. Which meant they dislocated more frequently from such things as walking a bit too fast or trying to carry something light. Which meant I did less. All on the grounds of 'your joints'.
As an adult (before the arthritis kicked off again), I went for physiotherapy. The main item the physio used in those first courses was a trampoline because they absorb the majority of the shock to the hypermobile joints, thus reducing the likelihood of further injury.
Wobble boards are fun, too - but nowhere near as effective at strengthening muscles and stabilising joints as trampolines.
Don't wrap him up in cotton wool and restrict him on the basis of his joints. He'll still hurt himself, it'll just be as a result of such things as putting one foot in front of the other. He'll learn to put them back in place, how to bandage/strap them. He'll not be best pleased about the frequent injuries, but believe me, if you're going to end up hurt anyway, it's worth it to actually have some fun rather than be isolated from your friends and all the things you want to do because of 'your joints'.